Either mathematics is too big for the human mind or the human mind is more than a machine.
I don't believe in natural science.
[Said to physicist John Bahcall.]
The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules.
...a consistency proof for [any] system ... can be carried out only by means of modes of inference that are not formalized in the system ... itself.
Gödel gave a formal demonstration of the inadequacy of formal demonstrations.
[An anonymous quotation]
Nothing new had been done in Logic since Aristotle!